Pith Number

pith:J4UVV2NX

pith:2026:J4UVV2NXNUPTEZDUISKSTYJUES

not attested not anchored not stored refs pending

Finite-sample Borel--Cantelli inequalities under mixing conditions

Chatchawan Panraksa

Explicit finite-N lower bounds for the union probability of events hold under quantitative mixing conditions.

arxiv:2604.23791 v2 · 2026-04-26 · math.PR

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\usepackage{pith}
\pithnumber{J4UVV2NXNUPTEZDUISKSTYJUES}

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3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We prove explicit finite-N lower bounds for P(∪_{k=1}^N A_k) when the σ-algebras generated by an event sequence satisfy quantitative ϕ- or α-mixing bounds. The main ϕ-mixing estimate is obtained by a residue-class blocking argument and a one-sided approximate-independence inequality; it has a free spacing parameter L≥0, spacing coefficient 1/(L+1), and residual terms governed by ϕ(L+1).

C2weakest assumption

The event sequence satisfies quantitative ϕ-mixing or α-mixing bounds (i.e., the mixing coefficients decay at a known rate), which is invoked to control the residual terms after blocking.

C3one line summary

Explicit finite-N lower bounds for union probabilities under phi- or alpha-mixing are proved via residue-class blocking with spacing coefficient 1/(L+1) and mixing residuals.

Receipt and verification

First computed	2026-06-09T02:07:27.351187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f295ae9b76d1f326474449529e13424b5e7d05eea865645b36e80d97a9009c3

Aliases

arxiv: 2604.23791 · arxiv_version: 2604.23791v2 · doi: 10.48550/arxiv.2604.23791 · pith_short_12: J4UVV2NXNUPT · pith_short_16: J4UVV2NXNUPTEZDU · pith_short_8: J4UVV2NX

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/J4UVV2NXNUPTEZDUISKSTYJUES \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 4f295ae9b76d1f326474449529e13424b5e7d05eea865645b36e80d97a9009c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b11bf877f8545b6380a16bcaa05eb70b48c6d950e2a9dc6f966df93400982f8",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-04-26T16:31:01Z",
    "title_canon_sha256": "ccd8604ababa03f9470973a1c13ed8dcebc9e9e33ec901793340142004994508"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.23791",
    "kind": "arxiv",
    "version": 2
  }
}